In connection with known thermostat valves, holding arms, on whose hook-shaped ends the cross arm is suspended, are attached to the cover-like housing member and project away from it. During operation, these holding arms are subjected to great stresses, so that the cover-like member is made of metal or a high-quality plastic material which can withstand these stresses. It is also known (DE 44 16 240 C1) to provide support elements on the main housing, to which the cover-like housing member is attached, and on which the cross arm is suspended during the assembly of the two housing members, so that the holding arms of the cover-like housing member are relieved. In most cases the main housing is an engine block or the housing of a water pump. Therefore, the manufacturer of the thermostat valve with the cover-like housing member is not the manufacturer of the main housing to which the cover-like housing member is attached. Thus, in many cases it is disadvantageous if the main housing must have a defined shape in order to take on the support function of the cross arm of the cover-like housing member.